Empirical and numerical analysis of small wind turbine ......Empirical and numerical analysis of small wind turbine aerodynamic performance at a plateau terrain in Kenya David Wafula

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Renewable Energy 90 (2016) 377e385

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Renewable Energy

journal homepage: www.elsevier .com/locate/renene

Empirical and numerical analysis of small wind turbine aerodynamicperformance at a plateau terrain in Kenya

David Wafula Wekesa a, b, *, Cong Wang a, Yingjie Wei a

a Institute of Dynamics and Control of Spacecrafts, School of Astronautics, Harbin Institute of Technology, Harbin City, PR Chinab Department of Physics, Jomo Kenyatta University of Agriculture & Technology, Nairobi City, Kenya

a r t i c l e i n f o

Article history:Received 28 February 2015Received in revised form3 November 2015Accepted 1 January 2016Available online 15 January 2016

Keywords:Aerodynamic performanceSWTCFDWPD

* Corresponding author. Institute of Dynamics andof Astronautics, Harbin Institute of Technology, Harbi

E-mail addresses: [email protected] (D.W. W(C. Wang), [email protected] (Y. Wei).

http://dx.doi.org/10.1016/j.renene.2016.01.0040960-1481/© 2016 Elsevier Ltd. All rights reserved.

a b s t r a c t

Kenya's energy depends on fossil fuels and the country is yet to embrace alternative sources that areenvironmentally friendly. In this paper, empirical and computational approaches are presented toinvestigate aerodynamic performance of Small Wind Turbine (SWT) operation at arid rural Mwingi-Kituiplateau region, Kenya. We used empirical statistics to represent wind resource, and Computational FluidDynamics (CFD) to address SWT aerodynamic performance at the site. The numerical simulations,employing Transition Shear Stress Transport (SST) model and fully mesh resolved rotor, were performedand results obtained compared with empirical methods. From the Wind Power Density (WPD) values,44.50e85.48 W/m2 between turbine hub heights 20 and 60 m, the site corresponds to wind class z1;hence unsuitable for grid-connected power generation. In addition, the numerical findings give usefulinsights to SWT aerodynamic performance with respect to empirical approach at a plateau terrain windregime.

© 2016 Elsevier Ltd. All rights reserved.

1. Introduction

Energy remains the major resource to transform a developingcountry into a developed one [1e4]. Kenya is a developing country,with energy mainly derived fromwoody biomass (68%), Petroleumfuels (22%), and electricity (9%) [5]. These competing energy sour-ces have impacted negatively on the environment. In addition,electricity, which is mainly hydro-power driven, is highly unreli-able. This is attributable to persistent droughts with consequentialdrying of water reservoirs [5]. Despite the country's struggle tosolve energy challenges, like establishing plants driven bygeothermal and diesel generators, energy cost continued to rise inthe last decade.

On average, National surveys have revealed that almost 90% ofKenyans rely on traditional fuels such as biomass, charcoal, anddung to meet their heating and cooking needs. Dependence onfirewood in the rural areas as the main source of cooking fuel is onthe rise, with more than 80% of households relying on firewood forcooking compared to 10% of urban households. Charcoal is the

Control of Spacecrafts, Schooln City, PR China.ekesa), [email protected]

second most popular type of cooking fuel used by 13.3% of house-holds, while Kerosene is the third and frequently utilized among44.6% of urban dwellers [6].

To reverse the trend of over dependence on fossils fuels, as wellas enhance access to cheap and reliable energy, there is need for thecountry to diversify its energy sources. In addition, new technolo-gies to harness local resources should be embraced to generateenergy. This will support economic development and promote self-sufficiency in energy needs with emphasis to the rural poor pop-ulation [5]. Wind energy is the latest veritable alternative energysource that is renewable for power production over the last decade,and offers the potential for CO2 emissions reduction in powergeneration [7e9]. For global CO2 emissions reduction to be realised,power generation should strongly depend on utilizing renewableenergy systems, especially in the developing countries.

However, effective use of wind energy requires precise windenergy resource assessment. Precise wind speed measurementsplays an important role for estimating the wind energy potential ofa target site. Generally, wind resource assessment includes[10e12]: onsite wind conditions measurement; correlations be-tween onsite meteorological towers to fill in missing data; corre-lations between long-term weather stations and short-term onsitemeteorological towers; analysis of the wind shear and its varia-tions; modelling of the distribution of wind conditions, and

D.W. Wekesa et al. / Renewable Energy 90 (2016) 377e385378

prediction of the available energy at the site.In Kenya, there is need for prospective and utilization of wind

energy resource as a solution to provision of sustainable, reliableand cost effective power to the rural areas and urban poor. One ofthe main challenge to exploitation of wind energy resource can beattributed to non-availability of the wind resource data in the ruralareas where the bulk of the country's population (84%) resides [13].Currently, the country has 34 national meteorological stationscentred in national airports and airstrips in urban areas [14].However, their data is gathered at meteorological height of 10 mand is intended for agro-meteorology and civil aviation and hencenot specific for harnessing wind as a source of energy [5,14]. Thus,in order to supply the increasing demand for the production ofelectricity especially for remote application, SWTs have an effectiverole [15].

Based on the 6 years data collected from four meteorologicalstations in Hong Kong, He et al. [16] investigated a surface windcharacteristics with different terrain conditions. Wind turbulentcharacteristics under different terrains were compared based onlong-term field measurements. From the study in Ref. [16], windcharacteristics which determinewind energy potential of a site, canbe significantly affected by surrounding terrains or topographies.Therefore, different upwind terrain or topographical conditionsmay result in remarkably varied distributions of local windresource and hence wind energy potential of a region. Similar ob-servations have been made in related studies in Refs. [1,17e24].

Using empirical methods, Mukulo et al. [5] and Kamau et al. [25]have analysed the wind energy potential for Marsabit and Mwingi-Kitui plateau, respectively, both Eastern regions of Kenya. Despitethe empirical methods being prone to many statistical errors, withlimitation in both time and cost, the studies results are very usefulto wind energy technology stakeholders [26]. However, unsteadyphenomena in the plateau terrains due to SWT rotational aero-dynamics cannot be investigated by classical tools, such as empir-ical and Blade Element Momentum (BEM) methods.

Therefore, in the present study, we seek to employ bothempirical and CFD approaches to evaluate aerodynamic perfor-mance of SWT operation at a remote power-starved population inrural Kenya. The results presented in this paper show that turbinehub height elevation has a very predictable influence on SWTaerodynamic performance through its effect on air density andkinematic viscosity. In addition, the numerical results providesdetailed understanding of CFD application and its added value inevaluating SWT aerodynamic performance with respect to empir-ical approach at a plateau terrain.

2. Methodology

2.1. Experimental techniques

Following the empirical study by Mukulo et al. [5], wind speedmeasurements were performed at a tower height level of 20 m,located at the Mwingi-Kitui plateau, Kenya. The plateau terrain siteis geographically located at an altitude of 0517 m above sea level onlatitude 1.000 S and longitude 38.010 E. Wind speed data weremeasured every 10 s and averaged at intervals of 10 min for storagein a data logger. The 10 min averaged wind speed data were furtheraveraged over an hour and stored sequentially in a permanentmemory for a period of 12 months. Furthermore, the wind speed athigher heights of 40 m, 60 m, 80 m, and 100 m could be calculatedusing the power law (Eq. (1)). The annual mean wind speeds forturbine hub heights were used as Umean of fluctuating wind, whilerespective standard deviations (ss) averages as fluctuation ampli-tude Uamp to represent the wind characteristics of the site [27].

The wind profile power law is a relationship between the wind

speeds at one height, and those at another. It is often used in windpower assessments where wind speed data at various heights mustbe adjusted to a standard height prior to use. The wind power lawwas used to convert the measured wind speed at 20 m elevation tohigher heights as in the case of an empirical study in Ref. [5]. Thepower law is expressed as:

vz ¼ v1

�zz1

�a

; (1)

where vz is the wind speed at height z and v1 is the reference windspeed at the reference height z1. The exponent a is an empiricallyderived coefficient that depends on such factors as surface rough-ness and atmospheric stability [28]. The value of the empiricalexponent varies from less than 0.10 for very flat land, water or ice tomore than 0.25 for heavily forested landscapes and typical value of0.14 for low roughness surfaces [2]. The value of 0.20 for exponenthas been chosen to describe the actual nature of ground cover at thesite. The empirical power law exponent of 0.20 fits within thedescription of the American Wind Energy Association (AWEA) for asitewith short grass, hedges and few trees which best describes theplateau terrain at the site [5].

2.1.1. Optical encodersAn optical encoder transducer was used to generate coded

reading of measurement. Shaft encoders were used formeasuring angular displacement and velocity. The anemometerand wind vane sensors in this study were developed using theincremental and absolute encoders, respectively, to generatedigital signals. Advantages of digital transducers over analogueones include high resolution, high accuracy, and relative ease ofadaptation in digital control systems. Details of the experimentalsetup involving calibration of wind sensors have been discussedin previous wind assessment studies by the authors in Wekesaet al. [28,29].

2.1.2. Measuring wind speed and directionThe wind sensors were clamped on a horizontal metallic

support masked on a strong metallic vertical stand 20 m abovethe surface. The wind sensors were separated well enough toavoid the flow disturbance due to the blowing wind. The signalsfrom both anemometer and wind vane sensors were fed to CR 10Campbell microcontroller-based data logger. Wind data wasmeasured and stored in the Electrically Erasable ProgrammableRead-Only Memory (EEPROM). Reading of wind speed was doneat interval of 3 times a day alongside conventional instruments atthe meteorological station for comparison. The language used bythe data logger is C which is a general-purpose programminglanguage that can work on any Automatic Voltage Regulator(AVR) microcontrollers. Detailed description of the softwaredesign and high resolution data logging instrumentation systemfor wind speed and direction measurement can be found inWekesa et al. [28,29]. The data logging system flow chart is asshown in Fig. 1.

2.1.3. Accuracy of measurementsA linear regression fit chart was used to test and establish a

correlation between the wind speed data by Mukulo et al. [5]meteorological anemometer with calibrated mast-mounted op-tical anemometer. The results of the comparison between twoanemometer measurements are displayed in the time series andscatter diagram shown in Fig. 2. The figure shows a very goodcorrelation between the data obtained by Mukulo et al. [5]meteorological anemometer with those of the experimentalmast-mounted optical anemometer. Therefore, Mukulo et al. [5]

Fig. 1. Data logging system flow chart.

D.W. Wekesa et al. / Renewable Energy 90 (2016) 377e385 379

wind data measurement is reliable to predict long term patternof wind regime. Furthermore, the strong correlation confirmsthat the experimental anemometer gives the correct readingsand practical readings can be approximated to the data from themeteorological station.

Furthermore, Mukulo et al. [5] obtained specific data for har-nessingwind resource at the site, and it was also revealed thatmostof the plateau terrain wind had mean speeds between 4 and 7 m/s.Observe from the wind speed frequency distribution in Fig. 3 that,the mean wind speed frequency ranged between 10 and 25%although in a small percentage. Most of the study months depictedabsence of both very low wind speeds between 0 and 2 m/s as wellas very high wind speeds (>9 m/s). From the wind speed frequencydistribution (Fig. 3), the most frequent wind speed is 5.5 m/sflowing for 25% of the total time in a year with usable quality wind(above 3.5 m/s) available for above 80% of the total study time. Theannual averages of shape k (dimensionless) and scale c (m/s) pa-rameters of the Weibull distributions were 3.54 and 5.45 m/srespectively [5].

2.2. Numerical techniques

2.2.1. The flow solverThere are three main forms of turbulence simulation methods

adopted in the CFD community, i.e. Direct Numerical Simulation(DNS), Large Eddy Simulation (LES), and Reynolds-AveragedNaviereStokes (RANS) [30e34]. Although DNS method is amongadvanced computational approaches in which all the space andtime scales are resolved, it requires a large amount of computingresources and time. The LES method is appropriate for 3D simula-tions hence still very computationally expensive to numericallyinvestigate the complex unsteady dynamics phenomenon due tothe 3D nature of the eddies [35e37]. Recently, more advanced CFDmodels are available, solving both three-dimensional (3D) and two-dimensional (2D) NaviereStokes equations for wind turbine aero-dynamics modelling [26,38e42].

Based on studies in Refs. [26,27,43], it has been shown that a 2Dmodel is sufficient enough in predicting the performance andaerodynamics that surround the Vertical Axis Wind Turbine

Fig. 2. Linear regression fit at a height of 20 m.

D.W. Wekesa et al. / Renewable Energy 90 (2016) 377e385380

(VAWT). In the present study, a 2D CFD model has been used torepresent the virtual wind tunnel; and unsteady RANS approachappears to be the most suitable to predict the aerodynamic per-formance simulations with an acceptable computational cost and,at least, reasonable accuracy. Therefore, a 2D incompressible un-steady CFD solver, based on finite volume method in the com-mercial software package ANSYS® Fluent®, is employed to solve thefull unsteady RANS governing Eqs. (2) and (3):

vuivxi

¼ 0; (2)

vuivt

þ ujvuivxj

¼ �1r

vpvxi

þ nv2uivxjvxj

�vu0iu

0j

vxi; (3)

where, i, j ¼ 1, 2. Here x1 and x2 denote the horizontal and verticaldirections, respectively; ui and uj are the corresponding mean ve-locity components; t is the time; r is the density of the fluid; p is thedynamic pressure; n is the kinematic viscosity; and u0iu

0j is the

Reynolds stress component where u0i denotes the fluctuating part ofthe velocity. The reader is referred in Refs. [26,32,44,45] for detaileddescription about unsteady RANS approach formulation.

2.2.2. Computational domain and solution methodologyThe CFD computational domain consists of twomesh zones; the

inner circular Rotor sub-grid zone and the rectangular outer zone.The two zones communicate via a pair of circular interfaces

Fig. 3. Wind speed frequency distribution w

between them. To this end, a User-Defined Function (UDF) sub-routine is developed and attached to the flow solver to controlthe dynamic mesh motion. The inner Rotor sub-grid zone iscomposed of three symmetric airfoil blades rotating at a commonangular velocity. The three airfoil blades are spaced equally at 120�

apart as shown in Fig. 4. The blades were defined as no-slip walls,while both interface boundary of the Rotor sub-grid and the outerrectangular wind tunnel sub-grid were set as an interface. No-slipwall boundary condition is used in this simulation to model thebottom and the top sides of the domain as was the case in Refs.[26,31].

From the wall distance study by Danao et al. [31], the side walldistance was set to 1.2 m from SWT axis test section (Fig. 4). Thevelocity inlet boundary condition from the test section was set to1.5 m, 0.3 m short of the 1.8 m in Wekesa et al. [26,27]. Since themodelled turbulence intensity decay in the simulations matchedthat of the experiments, this was not considered important. Likethe case in Refs. [26,27], the pressure outlet boundary conditionwas set to 3 m downwind to match the actual distance of the windtunnel fan from the SWTaxis of rotation [46]. The reader is referredto [ [26,27,31,47,48], and references therein] for full details ondomain boundary location with both mesh and time step inde-pendence preliminary studies.

Following blade thickness analysis study in Wekesa et al. [27],the airfoil coordinates of a National Advisory Committee for Aero-nautics (NACA) 4-digit (00XX) series symmetric profile of NACA0022 were imported to define the blade shape. A moving meshapproach with a sliding mesh technique was used for the rotationof the inner circular Rotor sub-grid zone in order to capture thetorque generated by the three blade airfoils [26].

From Fig. 4(b), the inner circular Rotor sub-grid zone coincidesexactly with the circular opening within the outer stationaryrectangular zone. The interface of the two mesh zone boundariesslide against each other with no excessive overlap to minimizenumerical diffusion, and have approximately the same character-istic cell size in order to obtain faster convergence [26,31,43].

The mesh was based on structured O-grid topology where thesize of the first cell height next to the wall was such that the yþ

values from the flow solutions did not exceed 1 [49]. This was thelimit of the turbulence model that was chosen for the simulations.The O-type mesh was primarily used in preference to conventionalC-grid topology because the expectedwake is not fixed on a specificpath relative to the blade; but rather varying greatly in directionswaying from one side to another side [26,31,50].

The coupled pressure-based solver was chosen with a secondorder implicit transient formulation for improved accuracy to solvelow-speed incompressible flows. All the governing equations forthe solution variables, which are decoupled from each other, aresolved sequentially. The Semi-Implicit Method for Pressure-LinkedEquations (SIMPLE) algorithm is applied as the pressureevelocity

ithin plateau regime for one year [5].

Fig. 4. An illustration of boundary conditions and meshes of the 2D numerical domain.

D.W. Wekesa et al. / Renewable Energy 90 (2016) 377e385 381

coupling algorithm. With respect to the discretization of the con-vection terms in the transport equations for the velocity and tur-bulence quantities, second-order upwind schemes are utilised[31,32].

The Green-Gauss cell based method has been employed forcalculating the gradients of the transport quantities on the faces ofthe cell boundaries. The under-relaxation factors are imposed toavoid numerical instabilities in the solution and their details arereported in Table 1. The turbulence intensity of inlet flow is set to11%with a turbulence viscosity ratio of 14. These conditions and thecomplete validation of the present numerical code is based on anempirical study illustrated by Mukulo et al. [5] at the site.

The present simulations required an average of about 20 sub-iterations to make the solution converge at each physical timestep. The time step convergence was monitored and the simulationwas considered to have converged when residuals of all conservedvariables fell below 1�10�5 [26,27,43]. The calculations were

Table 1Under-relaxation factors.

Pressure 0.2 [�]Density 1 [�]Body forces 1 [�]Momentum 0.7 [�]Turbulent kinetic energy 0.8 [�]Specific dissipation rate 0.8 [�]Intermittency 0.8 [�]Momentum thickness Re 0.8 [�]Turbulent viscosity 1 [�]

performed on a computer having, Intel® Core™ [email protected] GHz, 4 cores, 8 threads, physical RAM of 8 GB, andWindows 8 professional 64-bit operating system. Each simulationrequired a total Central Processing Unit (CPU) time of about 4 days.The details of the numerical set-up are reported in Table 2 for easiercomparison with other numerical experiments.

The Transition SST model was used for turbulent calculations, assuggested from recent studies by Wekesa et al. [26,27]. This wasattributable to its well behavior in adverse pressure gradients andseparating flow, which were typically seen during the unsteadywind inflow operation on a turbine rotor scale. In addition, theTransition SST turbulence model has shown a close positive per-formance prediction for simulating SWT transient flows [31,51,52].Detailed explanation for the turbulence model preliminary studiesincluding the assumption made can be obtained in[[26,27,31,47,48], and references therein]. Therefore, the TransitionSST model was employed for all the successive numerical simula-tions in this study.

3. Results and discussion

In the present study, five angular velocities are tested, rangingfrom 55.73 rad/s to 77.28 rad/s with free-streamwind velocities U∞from 4.24 m/s to 5.88 m/s. The corresponding turbine hub heightelevation range was from 20 m to 100 m in increments of 20 m,respectively.

3.1. Small wind turbine aerodynamic performance

The calculated values of wind power density (wind powerproduction per square area of a turbine) by the numerical methodwere compared with those of the empirical study in Ref. [5]. Higherhub heights were used to give higher wind power densities forpractical small-scale harnessing of wind energy. The numericalpower performance for the plateau site at various turbine hubheights above ground level is summarized in Table 3. The calculatednumerical blade average power PB and wind average power Pwranges from 3.06 to 15.26 W and 47.04e81.16 W at 40 me100 mturbine hub heights, respectively. However, at the lowest turbinehub height of 20 m, numerical PB and Pw are �0.27 W and 31.15 W,respectively, resulting into a negative power coefficient of �0.01.The largest positive CP performance of 0.19 is registered at 100 mturbine hub height with a highest prevailing mean wind speed of5.88 m/s. This is attributable to shorter bursts of high speed winds(gusts) occurring between the normal wind flow speeds rangingbetween 8 and 10 m/s [5,27]. The averaged numerical wind powerdensity WPD as a function of Pw over one wind cycle divided bySWT projected area A, defined as

WPDnumerical ¼PwA

¼ 12rU3

∞; (4)

matches the empirical wind power densities at all turbine hubheight elevations, hence confirming the reliability of the results.

From Fig. 5, both wind power densities varied uniformly across

Table 2Details of the numerical set-up.

Description Value

Air kinematic viscosity [m2/s] 1.8�10�5

Air mass density [kg/m3] 1.132Angular velocity [rad/sec] 55.73e77.28Free-stream wind velocity [m/s] 4.24e5.88Machine mean tip speed ratio [e] 4.6

Table 3Numerical power performance.

Hub height of turbine (m) 20 40 60 80 100Mean wind speed Umean (m/s) 4.24 4.88 5.30 5.62 5.88Fluctuating amplitude Uamp (m/s) 0.61 0.56 0.53 0.45 0.41Power coefficient CP �0.01 0.07 0.13 0.15 0.19Blade average power PB (W) �0.27 3.06 7.65 11.04 15.26Wind average power Pw (W) 31.15 47.04 59.83 71.23 81.16

Table 4Empirical and numerical wind power density.

Hub height Umean Uamp Wind power density

(m) (m/s) (m/s) (W/m2)

Numerical Empirical

20 4.24 0.61 44.50 43.240 4.88 0.56 67.21 65.860 5.30 0.53 85.48 84.380 5.62 0.45 101.75 100.5100 5.88 0.41 115.95 115.1

D.W. Wekesa et al. / Renewable Energy 90 (2016) 377e385382

the turbine hub heights with the numerical power density curverevealing slightly higherWPD. This can be attributed to the fact that2D vertical axis SWT models are essentially SWTs with infiniteblade aspect ratio AR which shifts the numerical power densityupwards, but the general shape is maintained [27,31,52,53].

Table 4 shows numerical and empirical power densities at fiveturbine hub heights with characteristic fluctuating amplitudes atrespective fluctuating mean wind speeds. The air density r for theplateau terrain based on temperature and height above sea level is1.132 kg/m3 [5]. Furthermore, from Table 4, the minimum tomaximum empirical WPD range falls within that of the numericalWPD range across the turbine hub heights.

Fig. 6 shows numerical power performances (PB, and Pw) acrossthe five turbine hub height elevations for the plateau terrain site.The available power in the wind increases with rising free-streamvelocity U∞ up to the maximum peak values generated within thefirst half cycle of the wind cycle at all turbine hub heights. After-wards, wind power plummets to its minimum value at all turbinehub height elevations in the second half of the wind cycle. In theplateau wind condition under study, a total of 9, 10.5, 11, 12, and12.5 rotor rotations completes one periodic wind cycle for fluctu-ating mean wind speeds Umean at hub heights 20, 40, 60, 80, and100 m, respectively. A detailed description and notations on thenumber of rotor rotations allowed to capture periodic convergencein one full wind cycle of fluctuation has been discussed in previousstudies by the authors in Wekesa et al. [26,27].

In addition, from Fig. 6, the maximum Pw peaks are 45.20, 63.78,78.51, 88.61, and 98.60W for turbine hub heights 20, 40, 60, 80, and100 m, respectively. These corresponds to maximum wind powerdensity peaks of 64.57, 91.11, 112.16, 126.59, and 140.86W/m2 (referto Eq. (4)). Therefore, as was observed in Refs. [27,46], the perfor-mance of a turbine in a fluctuating wind follows the wind velocity

Fig. 5. Turbine hub height versus wind power density.

variations.The wind power performance is further analysed in Fig. 7,

showing the distribution of the instantaneous power coefficient CP(rot),

CPðrotÞ ¼ PB12 rAU

3∞; (5)

as a function of rotor rotation for the SWT across the five hubheights. The blade average power PB is obtained from computingaverage of instantaneous blade power for the three rotor bladesover the periodic wind cycle at each turbine hub height elevation.

From Fig. 7, the unsteady plateau wind CP and quasi-steady CPare presented using moving average smoothing method as thewind fluctuates at various turbine elevations. Smoothing the un-steady CP is necessary as it provides comparative plots of CP per-formance across the various fluctuating wind speeds at differentturbine hub heights in the plateau environment. Furthermore,smoothing is shown to be consistent with the cycle-averagedmethod of computing for the rotor CP in steady wind conditions[27,31]. Hence, the fluctuating nature of the blade torque is filteredto give a single value of prediction of SWT aerodynamicperformance.

The unsteady plateau wind CP summary in Table 3 is revealed inmore detail in Fig. 7 where the quasi-steady positive CP is regis-tered across the turbine hub heights, except for 20 m turbine hubheight elevation with a fluctuating mean wind speed of 4.24 m/s.The results are in agreement to an empirical study by Mukulo et al.[5] at the site where positive wind performance was projected athub heights above 40 m. Following the low wind power densityvalues (Table 4), 44.50e85.48 W/m2 between turbine hub heights20 and 60 m, the plateau region corresponds to wind class z1.Similar details on wind power classification were revealed byKamau et al. [25] and National Renewable Energy Laboratory(NREL) [54] where wind power class z1 represented WPD rangebetween 0 and 200 W/m2 at 50 m turbine hub height elevation.Consequently, the plateau region is considered unsuitable for gridconnected power generation.

It is noteworthy that, in practice, the hub heights of small windturbines are certainly lower and cannot be installed at high towers(20e100 m), because they are typically designed to be used in ur-ban wind environment. Therefore, wind speed calculation at veryhigh turbine hub heights, 20e100 m, was performed to specificallyshow CFD numerical approach in addressing SWT aerodynamicperformances and its added value with respect to the empiricalapproach, rather than exploring site's suitability based on the SWTuse.

4. Conclusion

In this study, the empirical and numerical approaches have beenemployed to evaluate aerodynamic performance of small wind

Fig. 6. Power performances (PB and Pw) at different turbine elevations.

Fig. 7. Power coefficient at various turbine hub heights.

D.W. Wekesa et al. / Renewable Energy 90 (2016) 377e385 383

turbine operation at a remote power-starved population in ruralKenya. The small wind turbine aerodynamic performances at thesite have been analysed at five turbine hub heights. The empiricaland numerical wind power densities revealed a similar variationacross turbine hub heights for the plateau terrain region, with thenumerical method less prone to many statistical errors. Hence, thenumerical method is reliable in addressing the SWT aerodynamicperformances for the plateau region.

D.W. Wekesa et al. / Renewable Energy 90 (2016) 377e385384

At lowest turbine hub height of 20 m, numerical PB and Pware �0.27 W and 31.15 W, respectively, resulting into a negativepower coefficient of �0.01. In addition, because of the low windpower density values, 44.50e85.48 W/m2 between turbine hubheights 20 and 60 m, the plateau region corresponds to wind classz1; hence, the site is unsuitable for grid-connected power gener-ation. Compared to the prevailing empirical methods, the CFD nu-merical approach could be considered as an alternative,inexpensive and robust applicationmethod for addressing the SWTaerodynamic performance.

The numerical approach considers wind velocity fluctuations atthe site without assessing topology effects and the power responseof a small wind turbine to wind speed frequency distributionwithin the regime. Instead, the single frequency numerical model isintended to specifically elucidate the CFD application and its addedvalue with respect to the empirical approach. Therefore, futureworkwill be extended to develop amultiple-frequency-componentmodel to combine multiple frequencies within the wind regime.

Acknowledgements

This research work was supported in part by the Institute ofDynamics and Control of Spacecrafts, School of Astronautics,through the Harbin Institute of Technology; and the ChineseScholarship Council, through the People's Republic of China Gov-ernment (CSC grant no. 2013404003) in collaboration with theKenyan Government.

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